Artificial selection is an evolutionary drive that shifts the equilibrium state of the population under natural selection to a new state around the target. As a result, the phenotypic histories \({\bf x}_{t_0,\dots t_f}\)  over the period of \((t_0,\dots ,t_f)\)  are statistically distinct for evolution under natural and artificial selection (Fig. REF A). This deviation can be quantified by the Kullback-Leibler distance \(D_{KL} ({\mathcal {P}}_u ({\bf x})|| {\mathcal {P}}({\bf x}))\)  between the distribution of histories under artificial selection \({\mathcal {P}}_u({\bf x}) \equiv {\mathcal {P}}_u({\bf x}_{t_0,\dots t_f})\)  and under natural selection \({\mathcal {P}}({\bf x})\) . In the stationary state, the Kullback-Leibler distance quantifies the impact of artificial selection on evolution and can be interpreted as the amount of work \(W_{t_0}^{t_f}({\bf u})\)  done by external forces [1]} (i.e., the artificial selection) to shift the population from its natural equilibrium to the artificial equilibrium,
\(\nonumber W_{t_0}^{t_f}({\bf u})&=&D_{KL}({\mathcal {P}}_u ({\bf x})|| {\mathcal {P}}({\bf x})) \\&=&\int d{\bf x}_{t_0}^{t_f}\, {\mathcal {P}}_u ({\bf x})\log \left[\frac{{\mathcal {P}}_u ({\bf x})}{{\mathcal {P}}({\bf x})}\right] \) 
